An Introduction to Statistical Inference and Data Analysis

By Trosset, Michael W.

Book Id: WPLBN0000659897
Format Type: PDF eBook:
File Size: 0.9 MB
Reproduction Date: 2005

Title:	An Introduction to Statistical Inference and Data Analysis
Author:	Trosset, Michael W.
Volume:
Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago W. Trosse, B. M. (n.d.). An Introduction to Statistical Inference and Data Analysis. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: Mathematical Preliminaries: This chapter collects some fundamental mathematical concepts that we will use in our study of probability and statistics. Most of these concepts should seem familiar, although our presentation of them may be a bit more formal than you have previously encountered. This formalism will be quite useful as we study probability, but it will tend to recede into the background as we progress to the study of statistics.

Table of Contents
Contents 1 Mathematical Preliminaries 5 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Probability 17 2.1 Interpretations of Probability . . . . . . . . . . . . . . . . . . 17 2.2 Axioms of Probability . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Finite Sample Spaces . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . 32 2.5 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 43 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3 Discrete Random Variables 55 3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3 Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.4 Binomial Distributions . . . . . . . . . . . . . . . . . . . . . . 72 3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4 Continuous Random Variables 81 4.1 A Motivating Example . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3 Elementary Examples . . . . . . . . . . . . . . . . . . . . . . 88 4.4 Normal Distributions . . . . . . . . . . . . . . . . . . . . . . . 93 4.5 Normal Sampling Distributions . . . . . . . . . . . . . . . . . 97